Improve IsSubset for cyclotomic domains (such as Integers, PositiveIntegers, GaussianRationals etc.)

lib/cyclotom.gi

@@ -2065,6 +2065,31 @@ function (A,B)
 end );
 
 
+InstallMethod( IsSubset, "for a cyclotomic semiring and a range",
+             [IsCyclotomicCollection and IsSemiringWithOne,
+              IsRange],
+function (D, R)
+  local lo;
+  if IsEmpty( R ) then return true; fi;
+  # Ranges contain only integers.
+  if IsPositiveIntegers( D ) then
+    # PositiveIntegers contains all integers >= 1
+    lo := Minimum( R[1], R[Length(R)] );
+    return lo >= 1;
+  elif IsNonnegativeIntegers( D ) then
+    # NonnegativeIntegers contains all integers >= 0
+    lo := Minimum( R[1], R[Length(R)] );
+    return lo >= 0;
+  elif IsIntegers( D ) or IsRationals( D )
+       or IsGaussianIntegers( D ) or IsGaussianRationals( D )
+       or (HasIsWholeFamily( D ) and IsWholeFamily( D )) then
+    # These domains contain all integers, so any range is a subset
+    return true;
+  fi;
+  TryNextMethod();
+end );
+
+
 InstallMethod( Intersection2, "for certain cyclotomic semirings",
              [IsCyclotomicCollection and IsSemiringWithOne,
               IsCyclotomicCollection and IsSemiringWithOne],

tst/testinstall/cyclotom.tst

@@ -352,5 +352,45 @@ gap> SetX(r, r, {i,j} -> IsSubset(sets[i],sets[j]) = (i>=j));
 gap> SetX(r, r, {i,j} -> (sets[i]=sets[j]) = (i=j));
 [ true ]
 
+#
+# IsSubset for cyclotomic semirings and ranges
+#
+gap> IsSubset(Integers, [1..10^15]);
+true
+gap> IsSubset(Integers, [-10..10]);
+true
+gap> IsSubset(Rationals, [1..10^15]);
+true
+gap> IsSubset(GaussianIntegers, [1..10^15]);
+true
+gap> IsSubset(GaussianRationals, [1..10^15]);
+true
+gap> IsSubset(PositiveIntegers, [1..10^15]);
+true
+gap> IsSubset(PositiveIntegers, [0..10]);
+false
+gap> IsSubset(PositiveIntegers, [-5..5]);
+false
+gap> IsSubset(NonnegativeIntegers, [0..10^15]);
+true
+gap> IsSubset(NonnegativeIntegers, [-1..10]);
+false
+gap> IsSubset(NonnegativeIntegers, [1..10]);
+true
+
+# descending ranges
+gap> IsSubset(PositiveIntegers, [10,9..1]);
+true
+gap> IsSubset(PositiveIntegers, [10,9..0]);
+false
+gap> IsSubset(NonnegativeIntegers, [10,9..0]);
+true
+gap> IsSubset(NonnegativeIntegers, [5,3..-1]);
+false
+
+# empty ranges
+gap> IsSubset(PositiveIntegers, [1..0]);
+true
+
 #
 gap> STOP_TEST("cyclotom.tst");